This phrase dates back to the early 17th century. Used typically of a woman, it is now rather dated.

1998 - Spectator - She's no better than she ought to be. (British mothers of my generation often used that enigmatic phrase. They would use it about female neighbours of whom they disapproved or women in low-cut dresses on television.)

your better half

your husband or wife – humorous

seen better days = known better days

be in a worse state than in the past

have become old or worn-out or shabby.

so much the better

It is better for that reason.

so much the worse

It is worse for that reason.

1995 - Guardian - If you can get a tropical fruit juice, so much the better.